Question

10) Fatore os trinômios quadrados perfeitos abaixo: a) a2 + 14 a + 49 b) a2 - 14a +49 c) x + 16x + 64 c) x + 10x + 25 d) y - 12y + 36 e) t- - 4+4 f) 4r + 20r + 25​

Answer 1

$\large\boxed{\begin{array}{l}\tt a)~\sf a^2+14a+49\\\sf\sqrt{a^2}=a~~\sqrt{49}=7\\\sf 2\cdot a\cdot7=14a\implies trin\hat omio~quadrado~perfeito\\\sf forma~fatorada:(a+7)^2\\\tt b)~\sf a^2-14a+49=(a-7)^2\\\tt c)~\sf x^2+16x+64\\\sf \sqrt{x^2}=x~~\sqrt{64}=8\\\sf 2\cdot x\cdot8=16x\implies trin\hat omio~quadrado~perfeito\\\sf forma~fatorada:(x+8)^2\\\tt d)~\sf y^2-12y+36\\\sf \sqrt{y^2}=y~~\sqrt{36}=6\\\sf 2\cdot y\cdot6=12y\\\sf forma~fatorada:(y-6)^2\\\tt \end{array}}$

$\large\boxed{\begin{array}{l}\tt e)~\sf t^2-4t+4\\\sf\sqrt{t^2}=t~~\sqrt{4}=2\\\sf 2\cdot t\cdot 2=4t\implies trin\hat omio~quadrado~perfeito\\\sf forma~fatorada: (t-2)^2\\\tt f)~\sf 4r^2+20+25\\\sf\sqrt{4r^2}=2r~~\sqrt{25}=5\\\sf 2\cdot2r\cdot5=20r\implies trin\hat omio~quadrado~perfeito\\\sf forma~fatorada:(2r-5)^2\end{array}}$